Comparison of preconditioned Krylov subspace iteration methods for PDE-constrained optimization problems. Stokes control
type: Item
instance of: scholarly article
title: Comparison of preconditioned Krylov subspace iteration methods for PDE-constrained optimization problems. Stokes control
zbMATH Open document ID: 1365.65167
author: Owe Axelsson
author: Shiraz Farouq
author: M. Neytcheva
published in: Numerical Algorithms
publication date: 2017-01-12T00:00:00Z
review text: The authors investigate the optimal control of Navier-Stokes equations and concentrate on the arising linear system that can be compressed after eliminating the control function. They apply an efficient block matrix preconditioner and the condition number of the so precontioned matrix is bounded by 2 under certain contions. They show that their preconditioner has a better performance in terms of the number of iterations and execution time than other preconditioners on the same problem. This article is well written, structured and explained, it contains seven sections: Section 1 on Introduction, Section 2 formulates the control problems with a PDE contraint, Section 3 is about the precontioner and condition number bounds, in Section 4 a summary of some other preconditioning methods is presented, Section 5 covers a summary of computional complexity of the preconditioners, Section 6 contains the numerical results, Section 7 on Conclusion.
reviewed by: Başak Akteke-Öztürk
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 49J20
Mathematics Subject Classification ID: 76D05
Mathematics Subject Classification ID: 65F08
Mathematics Subject Classification ID: 65Y20
Mathematics Subject Classification ID: 49M25
zbMATH DE Number: 6674008
zbMATH Keywords: PDE-constrained optimization problems
zbMATH Keywords: finite elements
zbMATH Keywords: iterative solution methods
zbMATH Keywords: preconditioning
zbMATH Keywords: Navier-Stokes equations
zbMATH Keywords: computional complexity
zbMATH Keywords: numerical result
describes a project that uses: deal.ii
describes a project that uses: ParaView
describes a project that uses: Trilinos
MaRDI profile type: Publication
full work available at URL: s11075-016-0136-5
OpenAlex ID: W2279865210
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DOI: 10.1007/S11075-016-0136-5
description: scientific article; zbMATH DE number 6674008